Please, help me!

1)

The property 4 from book Cracking GRE (Chapter 6) says that if

a=b (mod n) is equivalent to a=b, b+(c-1)n (mod cn)

but I don't understand why?

2) A is a matrix with integer entries, det(A)=1, => the entries of the inverse of A will also be integers

why?

## Congruences anв matrices

If a = b (mod n)

then for every integer "c"

a = b + 2n (mod 2n)

a = b + 3n (mod 3n)

...

a = b + (c-1)n (mod (c-1)n)

a = b + cn (mod cn).

### Other Errors in Cracking the GRE...

I thought that must be an error also.

Other errors I found:

The chain rule example is completely wrong. If I let F(u,v,y) = z, u = f(v,y) and v = g(x,u), then I get the book's answer. Otherwise, there must have been a typo. Does that cohere with what others got?

Also, in Chapter 1, Cos(a+b) = cos a * cos b - (not +) sin a *sin b.

Were there any other glaring errors?

Other errors I found:

The chain rule example is completely wrong. If I let F(u,v,y) = z, u = f(v,y) and v = g(x,u), then I get the book's answer. Otherwise, there must have been a typo. Does that cohere with what others got?

Also, in Chapter 1, Cos(a+b) = cos a * cos b - (not +) sin a *sin b.

Were there any other glaring errors?

Yes this is a typo. But you've written it correctly here.Also, in Chapter 1, Cos(a+b) = cos a * cos b - (not +) sin a *sin b.

cos(a+b) = cosa*cosb

**-**sina*sinb

cos(a-b) = cosa*cosb

**+**sina*sinb

These are correct, while in the book signs in both eq. for cosine are opposite.

Btw. in

**some**(I have really seen it) books (3 ed.) there is one more typo on the same page a little bit above.

sin(-a) = -sin(a)

cos(-a) = cos(a).